CANINE DISTEMPER VIRUS IMPACT ON SERENGETI NATIONAL PARK LION-CHEETAH INTERACTIONS IN THE. By Aliénor Chauvenet. Dr. Sarah Durant Prof.

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1 CANINE DISTEMPER VIRUS IMPACT ON LION-CHEETAH INTERACTIONS IN THE SERENGETI NATIONAL PARK By Aliénor Chauvenet Supervised by: Dr. Nathalie Pettorelli Dr. Sarah Durant Prof. Tim Coulson A thesis submitted in partial fulfilment of the requirements for the degree of Master of Science and the Diploma of Imperial College London

2 ABSTRACT The impact of human-induced threats on biodiversity is a constant concern for the conservation community. Conservation projects are designed to decrease biodiversity loss by removing threats towards species or ecosystems e.g. the creation of protected areas to remove hunting pressure on a species. Sometimes, the creation of a protected area isn t enough and there is a need for additional human intervention e.g. removal of diseases or invasive species. The Serengeti National Park (SNP), which was created as a human intervention against game species depletion, is home to populations of two very charismatic cats: the African lion Panthera leo and the cheetah Acinonyx jubatus. In the plains of the SNP, they both persist in small populations. Unfortunately, the status of National Park is not enough to guarantee the survival of either population residing in the plains. The lion is vulnerable to a disease called canine distemper virus (CDV) due to the huge population of domestic dogs (reservoir for the CDV) surrounding the park. The cheetah, on the other hand, is under the pressure applied by lions as they kill cheetah cubs. There may be the possibility of eradicating the CDV from the Serengeti by vaccinating domestic dogs. However, the consequences of eradication on both cat populations need to be assessed first. I built two population models: an individual-based model for the cheetah and a matrix population model for the lion. I then investigated the consequences of different CDV outbreak rates on lion abundance and on cheetah population dynamics. I found that there seems to be a direct link between lion abundance and cheetah abundance. With the current outbreak rate (no interventions), the population of cheetahs in the Serengeti plains is decreasing and if the CDV is eradicated, they may go extinct faster. Cheetahs may even need an increase in CDV outbreak rates in order to be able to renew themselves. I found that with the current CDV outbreak rate or after CDV eradication, there would only be half the cheetah population left in 60 years. This project shows possible shortcomings of species-based human-interventions. By doing projects with the lion as sole focus (e.g. removing the CDV) conservationists may further endanger the cheetah. On the other hand, being focused on the cheetah might lead to promoting an increase in CDV occurrences which would in turn increase the chance to lose lions as small populations are more vulnerable to stochastic events. Further work should investigate how to optimally manage both species. Word count: 12,300 2

3 LIST OF ACRONYMS CITES CDV IBM(s) IUCN PA(s) SNP Convention on International Trade of Endangered Species Canine Distemper Virus Individual-based model(s) International Union for Conservation of Nature Protected Area(s) Serengeti National Park 3

4 CONTENTS I/ INTRODUCTION Problem statement Project significance Aim and objectives II/ BACKGROUND Study site and species Population Dynamics: a general overview Cheetah population dynamics: what has been done Lion impact on cheetah population dynamics: this project III/ METHODS Model description Lion matrix population model Cheetah individual-based model Coupling cheetahs with lions Simulations Testing model predictive power Effect of different CDV outbreak rates on the cheetah population IV/ RESULTS Model fitting Lion matrix population model (simulation a) Cheetah individual-based model (simulation b) Coupling cheetahs with lions (simulations c and d) Effect of different CDV outbreak rates on the cheetah population V/ DISCUSSION ACKNOWLEDGMENTS REFERENCES

5 FIGURES Figure 1. Average cheetah population growth rate over 100 simulations when the cheetah IBM is coupled with the lion matrix population model. Results depend on the simulation timeframe (60, 50, 40 and 30 years) and the number of outbreaks per 60 years Figure 2. Number of simulations where the populations have a negative growth rate (over 100 simulations). Results depend on the timeframe of the simulations (60, 50, 40 and 30 years) and the number of CDV outbreaks per 60 years Figure 3. Number of simulations where the populations have a positive growth rate (over 100 simulations). Results depend on the timeframe of the simulations (60, 50, 40 and 30 years) and the number of CDV outbreaks per 60 years TABLES Table 1a. Population projection matrix for the Serengeti lions for years when there is no CDV outbreaks. The reproduction rate F x =0.8 unless the population has reached its carrying capacity; in that case F x = Table 1b. Population projection matrix for the Serengeti lions for years where there is a CDV outbreak. The reproduction rate F x =0.8 unless the population has reached its carrying capacity; in that case F x = Table 2. Initial cheetah population composition Table 3. Monthly survival rates of the cheetahs in the Serengeti plains Table 4. Published female lions abundance in the Serengeti National park (inferred from Packer et al. 2005) Table 5. Expected ranking of r-squared values depending on which models are tested against observed cheetah abundance

6 Table 6. Simulation parameters for when the cheetah IBM is coupled with the lion matrix population model. Different outbreak rates are obtained by varying the CDV densitydependent trigger, the CDV random number trigger or both Table 7. Results of the lion model simulations (1000 iterations). The table shows the lion population growth rate for observed data (extracted from Packer et al. 2005) and predicted with the lion model (using the current parameters). The simulation timeframe is 29 years allowing for the calculation of the r-squared between predicted and observed data Table 8. Simulation results of the cheetah IBM without the varying influence of lions; r- squared is between model-predicted abundance and 16 years of observed adult males and females abundance (Sarah Durant pers. comm. Dataset ) Table 9. Simulation results of cheetah IBM coupled with lion published abundance (c). The lion data used are those observed from Packer et al. 2005; it provides lion numbers from 1975 to Hence, the predicted cheetah abundance is compared with observed date from 1991 to Table 10. Simulation results with current parameters of lion model (d); correlation between observed data (Table 4) and 16 years of predicted adult males and females abundance ( ) Table 11. Results of simulations (each of 100 iterations) of the cheetah IBM coupled with the lion matrix population model. + represents the number of cheetah populations for which the average (Av.) λ>or =1 and, - is the number of cheetah populations for which the average λ<1, / is the number of cheetah populations that went extinct Table 12. Average number of cheetahs surviving in the Serengeti plains after 60 years depending on how the number of CDV outbreaks during the timeframe

7 I/ INTRODUCTION 1. Problem statement The world s biodiversity is under threat and while the number of species on Earth and the rate at which they are disappearing remain uncertain, there is evidence that the current rate of species loss is much greater than historic ones (Millennium Ecosystem Assessment 2005). The principal causes for biodiversity loss are: habitat loss and degradation (including land conversion, deforestation, and pollution), habitat fragmentation, climate change, invasive species, overexploitation and diseases (Millennium Ecosystem Assessment 2005). The common element of all those threats is that they are all more or less human related. The impact of human-induced threats on biodiversity is under constant study and, conservationists have spent decades trying to halt or slow the rate of biodiversity loss. In order to do that, many conservation projects have been designed to remove threats towards species or ecosystems by using human interventions e.g. stop illegal logging (Hamilton et al. 2000), remove invasive rats on islands (Towns and Broome 2003). One of the first lines of defence against extinction is the creation of protected areas (PAs; Rodrigues et al. 2004). Protected Areas can take many forms e.g. they can be strict such as a National Park or they can be designed to accommodate regulated hunting like a game reserve. The motivations behind the creation of PAs are also varied e.g. protecting one patch of habitat, one species or an ecosystem function. The design of PAs always depends on the target and objectives the protected zone aims to achieve. Sometimes, the creation of a protected area isn t enough and there is a need for additional human intervention such as, for example, removal of invasive species (Foxcroft et al. 2007). One prominent example of human intervention is the Serengeti National Park (SNP), Tanzania. First created as a hunting-free game reserve in 1929 in order to stop the depletion of the Serengeti lion population, Panthera leo (Sinclair 1995), the SNP has now full protection status and is a safe haven for many species. The SNP is notably home to populations of two very charismatic cats: the African lion Panthera leo and the cheetah Acinonyx jubatus. Lions, which are the top predator of the SNP ecosystem, seem to be doing well in the park. Observations reported in Packer et al. (2005) show that beyond yearly variation in population size, the Serengeti lion population show an increasing trend. One of the threats to their survival in the park is a disease called Canine Distemper Virus (CDV). In 1994, an outbreak of CDV killed a third of the Serengeti lions (Roelke-Parker et al. 1996, 7

8 Woodroffe 1999). CDV exposure is however not always lethal, as studies of the Serengeti lion CDV seroprevalence showed that lions had been previously exposed to the virus without major death (Packer et al 1999). On the overall, the CDV affects four species in the Serengeti region: lions, spotted hyenas Crocuta crocuta, bat-eared foxes Otocyon megalotis and domestic dogs Canis lupus familiaris (Roelke-Parker et al. 1996, Carpenter et al. 1998) but has no incidence on the cheetah. Murray et al. (1999) found that the CDV is transmitted to lions and hyenas from the domestic dog which acts as a reservoir species. There are currently around 30,000 domestic dogs around the Serengeti (Roelke- Parker et al. 1996), and thus, the potential for a CDV outbreak remains constant. One way of reducing the impact of CDV on the Serengeti lion population is to vaccinate the dogs surrounding the SNP against the virus. Such procedure would go toward the conservation of the lion, a highly charismatic species which is classified as vulnerable on the IUCN red list (IUCN 2009). Cheetahs, which are on the Appendix I of the Convention on International Trade of Endangered Species of Wild Fauna and Flora (CITES), are also listed as vulnerable on the IUCN red list and have suffered from a range-wide decline in the past decades (IUCN 2009). Like other carnivores, they face several human-induced threats at the species level, notably habitat loss and persecution by humans (IUCN 2009). However, in the plains of the SNP, their population size is known to be limited by other factors. In the early 1980s, the SNP cheetahs were thought to be at genetic bottleneck: at that time, both little genetic variation and inbreeding were thought to be responsible for their low population number and survival rates (O Brien et al. 1985). However, in depth ecological studies proved that the low density of cheetahs was, in fact, due to cub being killed by lions and spotted hyenas (Caro 1987, Laurenson 1994; Kelly & Durant 2000). Laurenson (1995) found that lion predation is one of the biggest threats to cub survival and that cheetah biomass is inversely correlated with lion biomass across protected areas in the African sub-sahara, suggesting that lions play an important role on cheetahs number regulation. Beyond competing for food with the cheetahs, lions can also easily kill an adult (Laurenson 1995). However, they tend to attack the newborn cubs which are still in the lair, very often killing the entire litter (Laurenson 1995, Pettorelli & Durant 2007a). As lions were shown to be responsible for the very low cheetah cub survival rate in the SNP, and as cheetah biomass was previously reported to be inversely correlated with lion biomass across the African sub-sahara, I can safely hypothesize that variation in lion density should affect cheetah population dynamics. There are several examples, in nature, where the decrease or removal 8

9 of a top-predator has led to an increase of a mesopredator. The mesopredator release effect theory (Courchamp et al. 1999, Ritchie et al. 2009) states that as a community toppredator decreases or is removed, mesopredators are free to expand their niches as more food becomes available and/or predation pressure on its population decreases (e.g., the extinction of jaguars Panthera onca on Barro Colorado Island has led the puma Puma concolor and ocelot Leopardus pardalis shifting their diets to bigger prey, Moreno et al. 2006). However, although lions and cheetahs can compete for food, the reason for which cheetahs would benefit from a reduction in lions is not the resulting increase in food availability (Durant et al. in press). A decrease in lions numbers would result in the increase in cheetahs numbers because the direct predation pressure on cheetahs cubs would lessen. In the SNP, there are therefore two charismatic species that are equally loved by the international community and classified as vulnerable on the IUCN red list (IUCN 2009). The problem resides in the fact that (1) although they are increasing on the overall, the SNP lions number remains below 200 (Packer et al. 2005) which make them particularly vulnerable to environmental stochasticity, therefore, to a new epidemic of CDV (Kendall 1998) and (2) the cheetahs number are also very low (less than 100 adults; Sarah Durant pers. comm.), they have previously been found to be decreasing and their number is known to be limited by the lions (Kelly and Durant 2000). As population sizes within a guild are limited by competition, predation or a mix of both (Holt and Pickering 1985) and as a factor affecting one species population size can end up affecting the entire guild (Levin 1970), a CDV outbreak (or the disappearance of such a virus) could greatly impact the lion numbers and in return the cheetah numbers. It is expected that the higher the number of CDV outbreaks the lower the number of lions and therefore the higher the number of cheetahs. On the other hand, the total removal of the CDV could lead the lion population to increase and the cheetah population to further decrease. Before considering human-intervention such as the vaccination of the domestic dogs against CDV, there is a need to assess the consequences that eradication would have on the populations of cheetahs and lions in the SNP. By being species driven, human intervention in the SNP could lead to unintentional conservation triage (Possingham 2002), that is, prioritizing one species over the other leading to the disappearance of the non-target. 9

10 2. Project significance The world biodiversity is declining (Millennium Ecosystem Assessment 2005). As a response to threatened biodiversity, protected areas have been created to protect species under threats (Lee and Jetz 2008). The SNP is protecting the lions by removing human pressure on this much-loved species. However, due to the laws of predation and competition, while lions are fine, cheetah numbers are not increasing, especially in the Serengeti plains, leading to the belief the Serengeti cheetah survival depends on the lion population remaining at a certain level. A natural form of control over the Serengeti lion s population number is the Canine Distemper Virus. While the CDV is always silently present in the lion population, it can eventually lead to an epidemic; it did in 1994, reducing lion numbers by a third (Roelke-Parker et al. 1996). However, there is the possibility of eradicating the CDV from the Serengeti, removing the control over the lion population. This could have catastrophic consequences for cheetahs in the Serengeti plains. There is therefore an obvious conflict. While conservationists want nothing more than protect the world species, good-intentioned human intervention could cause the accidental disappearance of a whole population. As a result, understanding the effect of variation in the lion population on the cheetah population can lead to being able to predict the response of the cheetah population if the lion population increases (e.g. due to an increase in preys or the disappearance of the CDV) or decreases (e.g. after a CDV outbreak). 3. Aims and Objective This project aims at understanding the impact of variation in the SNP lion abundance on the SNP cheetah population numbers by modelling the cheetah population dynamics when coupled with a lion population undergoing different CDV epidemic rates. In order to reach that aim, I will: 1. Build an age-structured matrix population model for the lion population where I can control the number of CDV outbreaks hitting the population over time. 2. Build an individual-based model for the cheetah population where individuals have different survival and reproductive abilities. 3. Couple both models and investigate the effect of variable occurrence of CDV outbreaks on lion and cheetah population dynamics. 10

11 II/ BACKGROUND 1. Study site and species The Serengeti is a 30,000 km² ecosystem that extends over the border between of Tanzania and Kenya; it is defined by the migration range of the wildebeests, Connochaetes taurinus (Sinclair 1995). The main feature of this exceptional ecosystem is the amount of biodiversity that resides within it. In addition to high diversity of carnivores (the largest concentration in the world) and birds, there are 28 species of ungulates living in the Serengeti and herds are bigger than anywhere else in the world (Sinclair 1995). There are several conservation administrations within this ecosystem: Ngorongoro Conservation Area, Serengeti National Park, Maswa game reserve, Masai Mara National Reserve. The SNP was established in the early 1950s, following the region being declared a hunting-free game reserve (Caro 1994, Sinclair 1995). Although, at the beginning, it encompassed the Ngorongoro craters and its northern limit stopped below the Kenyan border, since 1965 the national park has ceased to include the former and has been extended to include the current Kenyan outstretch. This project focuses on two species: the cheetah and the lion. They both occur throughout the SNP but I will focus on the populations that live in the Serengeti plains. These grassy plains are located in the south-eastern part of the SNP and cover an area close to 5,000 km² (Caro et al. 1987, Caro 1994). In the SNP, cheetahs are found in both the plains and the woodlands, however, there is extensive observational data on the plains population. Their lifecycle can be divided into four stages: pre-weaning small cubs (1 to 3 months old), large cubs (4 to 12 months old), adolescents (13 to 24 months old) and adults (>2 year of age). Cheetah females are solitary and occupy overlapping home ranges, while males can be solitary, territorial, and/or form coalitions (Caro 1994). Male territory size averages 48 km², whilst solitary males and females can range over 800 km² (Caro 1994). From two years old, female cheetahs are reproductively active. The largest litter ever recorded is seven cubs (observed once; Sarah Durant, pers. comm.) but usually the maximum of cubs produced per litter is six (Kelly and Durant 2000) Females can become pregnant before the current litter leaves the mothers side, however, the family will separate before the new cubs are born. If the female loses a litter, she can enter oestrous rapidly (Caro 1994) and produce a new litter in about 4 months (Crooks et al. 1998). Once the adolescents have left their mothers, they can stay in a sibling group for up to 6 months, after which females leave to be solitary and have their first litter (Caro 1994). During the first year, and particularly the 11

12 first two to three months, cubs are extremely vulnerable to lions attack (Laurenson 1994). The lions will usually kill the whole litter (Laurenson 1995). The pressure that lions inflict on cheetahs is such that in 1994, Laurenson recorded that of all the cubs death that could be attributed a reason, a bit less than 70% was due to lion killing them. The relationship between cheetahs and lions is one of occasional competitors but mostly predator-victims: as lions do not feed on the cubs they kill, the word prey doesn t describe the situation accurately, and hence cheetahs should more accurately be referred to as lions victims. Lions are territorial, highly social species. They live in prides that are composed of 2 to 9 adult females and 2 to 6 adult males (Hanby et al. 1995). In addition, the prides contain the females dependent young. In the SNP, lions reside in the plains and the woodlands alongside the cheetahs. Lions feed principally on migratory species such as wildebeest and zebra, Equus burchelli, and therefore endure high fluctuations in food availability (Scheel and Packer 1995). Females can start reproducing once they reach four years of age and can live up to 18 years old (Clutton-Brock 1988). Both species have been studied for decades (Scheel and Packer 1995, Durant el al. 2007). There is, therefore, extensive information available on them in the published literature. Records of cheetahs abundance (adults and adolescents of both sexes) for the period of 1991 to 2006 have been obtained from Sarah Durant (pers. comm.) while lion abundance was recovered from Packer et al. (2005). 2. Population dynamics: a general overview To study population dynamics is to investigate how a population composition evolves over time (Williams et al. 2001). At its simplest, the number N of individuals in a population at time t+1 depends on the number of individuals at the time-step before (time t) and the birth and death that have occurred in the transition from t to t+1. If the population is not isolated from others, individuals can join or leave it, also influencing the population composition. Therefore: (1) Slightly more complicated mathematical models have been created to better describe the dynamics of a population. Equation (2) below, is best suited for populations that have breeding seasons where there is a sudden population increase at a regular time-step. In such approach, the population at the next time-step t+1 is defined as a function of the population at the current time-step N t and the finite population rate of growth λ: 12

13 (2) The parameter λ determines the trajectory of the population. If λ=1, the population is replacing itself whereas if it is λ<1, the population is decreasing over time. However, if λ>1, the population is increasing. On the other hand, equation (3) is more suited for populations that breed all year long with no sudden increase. The population composition at t+1 is once again determined by N t but also by the intrinsic growth rate r. Here, (3) The relationship between the finite growth rate λ and the intrinsic growth rate r is: (4) Those simple equations, however, describe populations with unrestricted growth, which would equal to an infinite supply of resources (food, habitat, etc...). Moreover, equations (2) and (3) assume that the birth and death rates are constant and that all individuals can be described with the same parameters values because they re considered as being equal (no individual heterogeneity). By considering all individuals to be equal (over time and space), equations (2) and (3) assume that the population is not under the influence of demographic or environmental stochasticity. Demographic stochasticity represents the variations between individuals within the population that result from random events in survival and reproduction (e.g. some individuals will survive longer or have more offsprings; Shaffer 1987, Kendall 1998). Environmental stochasticity represents variations that result from the weather, food supply or populations of competitors and predators (Shaffer 1987; Kendall 1988). Demographic and environmental stochasticities both occur to different extent in every species and ignoring them can lead to a poor representation of a system. To attempt at modelling population dynamics closer to reality, there are equations that take into account the fact that population growth isn t infinite. The logistic growth rate equation incorporates a new parameter: K or carrying capacity. The carrying capacity represents the number to which the population can grow before density-dependent selfregulation forces the population to stabilise (Fowler 1981). K can be determined by many factors (e.g., food availability, predator number). As a result the value of K can vary temporally for the same population. To simplify the use of the carrying capacity, its value is generally assumed to be constant while the self-regulation response to reaching K is assumed to be immediate. In such situation, the population growth model can be described as: (5) 13

14 Equation (5) can also be adjusted to describe a population that is harvested by removing a portion of the population at each time-step. It has, in addition, been adapted to model two common interactions between populations: prey-predator and resource competition. Those two models are called: Lokta-Volterra transition equation and Lokta-Volterra completion model respectively (Williams et al. 2001, Rockwood 2006). So far, I have described models where no individual variability is considered. It is however possible to incorporate some of this variability by aggregating individuals according to their sex or age, creating models with increased predictive power. The idea is to divide the population into smaller units of individuals sharing a trait or character. Instead of approximating one intrinsic growth rate for the entire population, variation in r is allowed by e.g. attributing different values of r to every age category. Let s consider for example a population whose individuals can be aggregated in x=3 age categories. Each age category has an individual intrinsic growth rate r x and a number of individuals N x at time t. At time t+1, the total population is therefore composed of: Equation (6) describes the composition of the entire population by considering each age category to be isolated, hence individuals can t move from one to another in the course of their lives. However, individuals do move from one age category to another as they grow older. To model a population where there is a transition between age categories, the population s life cycle needs to be identified (Caswell 2001). The two key parameters of life cycles are reproduction and survival; these are also called vital rates and can be defined as age- and/or sex-specific. Those vital rates will have different influences on the dynamic of a population. For example, the factors that have the strongest influence on cheetah s population dynamics are adult and cub survival (Kelly and Durant 2000). In order to determine which parameters are most important for a population, a perturbation analysis can be performed. Its results are expressed as sensitivities and elasticities (Caswell 2001, Caswell 2009) e.g. the sensitivity of λ to adult survival. Sensitivity informs on how a parameter y will change if a parameter x changes. Elasticity is the proportional response of a parameter to a proportional change in another (Caswell 2001). Life cycles are used in matrix population modelling (Caswell 2001). A matrix is built following a fundamental principal: a population will grow over time but not without limits. As a result a matrix population model can account for a small amount of individual heterogeneity and also be density-dependent. The population is divided into classes of (6) 14

15 similar individuals. To design the matrix, the population is divided into discrete classes to which we will apply class-specific parameters. At time t the population will be composed of a certain number n of individuals in each class x nt. The aim is to project the number of individuals at time t+1. At time t+1, the individuals that were in classes x t at time t will have moved to class x t+1 if they survived and new individuals are born and enter the matrix. Matrix based models have often been used in the literature to solve various problems. For example, O Connor et al. (1993) used a size-structured matrix population model to investigate the population growth rate of six perennial African grasses under different fire regimes. In 2000, Bro et al. used matrix modelling to look at the state of French populations of the grey partridge Perdix perdix. This type of population modelling was also used to study the reintroduction success of the black-footed ferret Mustela nigripes in Northern America, establishing that the first year survival rate is the most important rate for the ferret persistence (Grenier et al. 2007). Matrix population models were also used to look at the fire management and density dependence of the restoration success of longleaf pine forest Pinus palustus in the US (Cropper and Loudermilk 2006). There is another option for modelling population dynamics; one that allows for true individual variation: individual-based models (IBMs). Like matrix models, IBMs have been used in ecology for years (Grimm et al. 2005b, Nehrbass and Winkler 2007). While the former utilizes a top-down approach, that is, model the population to infer things about the individual, the latter uses a bottom-up approach. Indeed, in individual-based modelling, the smaller parts of a system are assembled first, the individuals, in order to infer things about the entire system: the population (Grimm 1999, Reuter et al. 2005). Ecological systems are complex entities and using simpler models sometimes isn t enough to capture the relationships that need to be represented. Some of the problems with more classic models (as opposed to IBMs) are that they don t account for the high number of components of the system and their variability, the spatial and temporal scale within which species operate, context-sensitive actions or feedback loops such as, for example, how density-dependence might influence future generation size (deroos et al. 2003, Reuter et al. 2005). Non-individual-based models have a lot of generalization potential but it comes at the cost of closeness to reality. IBMs on the other hands are more flexible but require more data to implement. The definition of an individual-based model is a simulation model that treats individuals as unique and discrete entities that have at least one property that changes during their life cycle beside age e.g. weight, predation susceptibility, reproductive output (Grimm 1999, Grimm and Railsback 2005). Therefore, by allowing for 15

16 individual variability, IBM can be closer to reality but also more complex. As a result it is essential to find the right balance between the amount of details and the general application of the model. Indeed, the more details in the model the more complex and case-specific it is going to be; hence less likely to be used to derive general ecological rules. However, by reducing the amount of details too much, there is the risk of losing the benefits of treating each individual as unique, like they actually are: better representation of reality (Grimm and Railsback 2005). There are no standards in constructing an IBM like there is for matrix models and IBMs require an amount of data that is not available for all species. That type of modelling cannot, therefore, always be used to model an ecological system. As there are no standard guidelines to build an IBM, the construction of one must rely on patterns that have emerged from the observations of the system the model is trying to represent. Patterns are rules that will determine how each individual will evolve spatially or temporally (Grimm et al. 2005, Grimm 1999). There are several limitations to using IBMs; as pointed out before, there is a trade-off between the complexity of the model and how it will be possible to interpret it. IBMs are also not easily described by mathematical formulas and common language, which makes it hard to communicate the results or allow for verification and replication by others. The data requirement is extensive and rarely available. Moreover, if adequate data is available, IBMs are highly specific as opposed to generalized modelling. Finally, the lack of standards results in models built from scratch using ad-hoc assumptions (Grimm and Railsback 2005). Regardless, IBMs have been used exponentially since 1988 when Huston et al. published a review criticizing modelling assuming that individuals making up a population are identical and that each individual has the same interaction with all its conspecifics. Since then, IBMs have been used in varied situations e.g. model fish reproductive output (Scott et al. 2006), investigate the impact of biological control on an introduced plant (LeMaitre et al. 2008), explore tree-tree intraspecific competition (Caplat et al. 2008) and model predator-prey interactions in a small rodent community (Reuter 2005). Moreover, in 2007, Nehrbass and Winkler used individual-based modelling to assess the spread of the invasive German hogweed Heracleum mantegazzianum. They compared their results to a previous simpler matrix model and found that modelling individuals as autonomous entities made the results closer to reality. 16

17 3. Cheetah population dynamics: what has been done There have been a few attempts at modelling the population dynamics of the cheetah. In 1995, Laurenson attempted to look at cheetah population dynamics in the SNP using a simple mathematical model of birth, death and recruitment, and found that high juvenile mortality severely limits cheetah abundance. Berry et al. (1997) found concurrent results through a population viability analysis (PVA; using Vortex, Lacy et al. 2005), estimating that the cheetah population of Namibia is limited by cub mortality but also adult humaninduced mortality. In 1998, Crooks et al. created an age-structured matrix population model with data from the Serengeti cheetah and came to a different conclusion, saying that actually, adult mortality has the most influence on cheetahs population numbers. In 2000, a more complex PVA was conducted by Kelly and Durant (2000). They used long-term demographic data (20 years observation data) on the SNP cheetahs to estimate the population growth rate (λ). They also analysed cheetahs extinction risk using the stochastic model Popgen (Durant 1991) and investigated the effect of different lion densities on juvenile survival. They came to the conclusion that (1) the Serengeti cheetah population growth rate is most sensitive to adult and juvenile survival, (2) the population growth rate λ was close to 1 (λ =0.997) during the 20 year study ( ), revealing no strong population trend, and (3) high lion abundance (the highest ever recorded during the study: 120 adult females) would lead to cheetahs going extinct in the next fifty years. All these attempts at understanding cheetah population dynamics have highlighted the fact that the juvenile and adult survivals have a major role in limiting cheetah numbers. However, according to Kelly and Durant (2000), cub survival is much more likely to vary than adult survival making cub survival the most determinant factor in cheetah population dynamic. These models, nonetheless, do not take into account the high individual variability in survival and reproduction previously reported in cheetahs (Caro 1994; Pettorelli & Durant 2007a,b; Durant et al. in press). It is expected that better integrating individual variability in cheetah population dynamics models would increase the predictive power of the models. One way to model individual variability is to use individual-based modelling. With a small population like the cheetahs in the Serengeti plains that has been studies for several decades, IBM seems to be a highly feasible and appropriate choice. 4. Lion impact on cheetah population dynamics: this project For this project individual-based modelling will be used to model the dynamics of the cheetah population of the Serengeti plains. I have a dataset containing 16 years of 17

18 population monitoring (number of adults and adolescents of both sexes each year; Sarah Durant, pers. comm.). In addition, the cheetah is a very well studied species, providing me with published demographic information usable in the model. From those published studies (Crooks et al. 1998, Kelly and Durant 2000, Durant et al. in press) have arisen patterns that can be used in this model, guaranteeing the right amount of complexity and limited uncertainties. One of the main criticisms addressed at IBM is the lack of generality. This model purpose is to be a predictive tool for the Serengeti cheetah population, which allow us to be species-specific. IBM performance can be tested against the observed population numbers from the 16 years dataset by calculating the population growth rate λ and r- squared between observed and predicted adult male and female numbers. As far as the Serengeti lions are concerned, matrix population modelling will be used as a simpler way to model their population dynamics. The lion matrix population model will be a female-based age-structured model and will take into account the impact of canine distemper virus on lion abundance. By creating a model for the lion population (instead of using lion numbers as covariates for example) I can control the number of CDV outbreaks during a given period of time. The occurrence of an outbreak is controlled by two factors: density-dependence (the lions must have reached a certain number) and stochasticity (there is a random chance that even if the population reaches the right abundance an outbreak will actually not occur). The lion matrix population model does not account for the fact that lions are organised in prides. The highly structured nature of lion population plays an important part in female survival and reproduction as both depend on territoriality and synchronous breeding (Packer et al. 2001). I, however, have to rely on published data to create the model and cannot make the lion model as realistic as it would need to be. As a result, it is going to be less accurate. Those two models will then be coupled to investigate the link between lion abundance and cheetah abundance based on the fact that (1) lions influence the cheetah cubs survival rate (0 to 1 year old) and (2) the CDV plays an important role in regulating lion numbers. 18

19 III/ METHODS 1. Model description 1.1. Lion matrix population model I used a female-only age-structured matrix population model (assumes a 1:1 ratio of females to males) to represent the Serengeti lions population (x=18 age classes of one year). According to Ogutu et al. (2002), the lion population composition is: 20% small cubs (0 to 1 year old), 10% large cubs (1 to 2 years old), 15% sub-adults (2 to 4 years old) and 55% adults (>4 years old). I used an initial population number of 35 females based on the population number reported in Packer et al. (2005) and split the initial female population according to the percentages above e.g. 10% in the 0-1 class, 20% in 1-2 class, (15/2)% in 2-3 and 3-4 class, (55/14)% in the remaining classes. I inferred the lion age-specific survival rates and CDV mortality rates in the Serengeti from Kissui and Packer (2004; Table 1a and b). Lions can reproduce once they enter the 3 to 4 age class (once they have survived beyond 3 years old; Clutton-Brock 1988) until they reach 13 years old. The reproductive rate is the same for every reproducing class x: F x = 0.8 females (Clutton-Brock 1988). The model is density dependent. Based on values reported in Packer et al. (2005), the initial carrying capacity was set as 60 females but it can vary throughout the simulation as a way to replicate bad, average and good years (e.g., a good year can be a wet year when there are a lot of prey as opposed to a dry year when prey density is lower). If the carrying capacity is at 60, it can drop to 40 or increase to 80; there is an equal chance of either. As I do not have quantitative data on changes in carrying capacity and there is no obvious pattern emerging from the data presented in Packer et al. (2005), the most sensible way to vary the carrying capacity from 60 is, therefore, to give it an equal chance of increasing or decreasing. If the carrying capacity is at 80, it can only decrease to 60 and if it is 40, it can only increase to 60. This ensures that the changes are not too dramatic. The change in carrying capacity is triggered by the comparison between a random number (taken from a uniform distribution) and a set trigger number. I use the number 0.8 as a trigger for a carrying capacity change. The choice of trigger number is based on a rule of thumb rather than empirical data. From Packer et al. (2005) it seems that the carrying capacity changes less often than every year. Therefore, I chose a number that makes a change relatively rare. If the random number is >0.8, the carrying capacity changes according to the pattern described above. If the total number of females at time t is equal to or above the carrying capacity at the current time-step, it is assumed that the shortage of resources will prevent 19

20 the population from increasing. The actual consequences of reaching K haven t been quantified for the lion (at least in available published data); however, there is a supported theory that states that as a population reaches its carrying capacity one consequence is a decrease in reproductive rate of adult females (Eberhardt 2002) and I modelled the impact of reaching at carrying capacity by setting the next time-step fecundity to zero: F x(t+1) =0 (Table 1b). An outbreak of CDV becomes possible when the female number is equal or above 60 which simulates the population susceptibility to being infected, e.g. the higher the density of lions the higher the chance to come in contact with an infected animal (Packer et al. 1999). I used a density-dependent CDV trigger since in Packer et al. (2005), the 1994 epidemics which claimed a third of the Serengeti lions happened after a peak in population number, supporting the hypothesis that CDV outbreaks have a density-dependence component. If the population reaches 60, the model compares a random number (from a uniform distribution) to a number trigger of 0.8 which simulates the need for a certain number of infected individuals to get an epidemic; the higher the CDV trigger is the harder it is to have an outbreak. If the random number is above 0.8, the population suffers from a CDV outbreak and the survival rates used to project the population from t to t+1 are the one from Table 1b. Based on published data, there has been 1 epidemic in 29 years (in 1994) and by using both CDV parameters of 60 females and number trigger of 0.8 I managed to simulate 2 epidemics in a 60 years time frame which is close to reality. The population can be projected over any timeframe but in order to compare the model predictions with the values reported in Packer et al. (2005) from 1975 to 2003, I used a 29 years timeframe. The simulations were run over 1000 iterations. For the lion population model alone I calculated the population growth rate λ. In order to do that, at each time step t, I determined the ratio:, N being the total number of individuals in the population and take the average of all the values obtained. The λ from the observed values reported in Packer et al. (2005) is 1.05, and I expected the λ of the model to show an increasing population trend as well. I also calculated the mean r-squared between both observed and predicted lion abundance. 20

21 Table 1a. Population projection matrix for the Serengeti lions for years when there is no CDV outbreaks. The reproduction rate F x =0.8 unless the population has reached its carrying capacity; in that case F x =0. x F 3-4 F 4-5 F 5-6 F 6-7 F 7-8 F 8-9 F 9-10 F F F F

22 Table 1b. Population projection matrix for the Serengeti lions for years where there is a CDV outbreak. The reproduction rate F x =0.8 unless the population has reached its carrying capacity; in that case F x =0. x F 3-4 F 4-5 F 5-6 F 6-7 F 7-8 F 8-9 F 9-10 F F F F

23 1.2. Cheetah individual-based model Conversely to the lion population model, the cheetah individual-based model accounts for both males and females. The population is structured in four categories: 0-3 months old (small cubs), 4 to 12 months old (large cubs), 13 to 24 months old (adolescents) and >25 months old (adults). The model follows each individual throughout their life cycle by monthly increments. The initial population number and composition correspond to year 1991 of the dataset available on the Serengeti cheetahs (Sarah Durant pers. comm.; see Table 2). The dataset, however, does not contain the number of 0-1 year old cubs as it very hard to estimate cub abundance for two reasons: during the first 2 to 3 months of life the small cubs stay hidden in the lair and births can be unrecorded if the mother is not spotted at the right time (Kelly and Durant 2000). After performing a 12-months simulation (100 iterations), I found that the average annual number of cubs produced is around 60. The sex ratio being 1:1 (Caro 1994), I started the population with 30 cubs of each sex. Nonetheless, after trying with several initial cub number (from 10 to 60 per sex), it appeared that this number had very little influence on the model performance. Table 2. Initial cheetah population composition Age group (in months) Males Females The monthly survival rates of each age-class were extracted from published literature (see Table 3). However, the survival rates of the small cubs (0-3 months old) published in Crooks et al (1998) and Kelly and Durant (2000) are both very small (0.03 and 0.10 yearly survival rate respectively). Those rates come from observed data on a rarely seen age-group (Caro 1994) have been measured under lion influence. For this IBM, I included a correlation between small cubs death in the same litter (if one cub dies, the entire litter dies too; Laurenson 1994). As a result, I started by setting the small cub survival to be the same as large cubs. The correlation adding pressure to the small cubs survival rate, it reduces it and sets a greater pressure on small cubs than large ones. Depending on the age-group they currently are in, each individual is assigned a probability of survival taken from the normal distribution of Table 3 s means and standard deviations. At each time-step and for each individual, a random number (from a uniform distribution) is generated and compared with 23